In many applications typically arising from natural and social sciences [1]}, [2]}, however, the likelihood functions \(p(y_{\mathrm {obs}}\vert \theta )\)  concerning probabilistic models are intractable.
In state space-space models [3]}, the likelihood function is an intractable high-dimensional integral over the state variables governed by a Markov process. Approximate Bayesian computation (ABC) introduced in [4]} is a popular approach for Bayesian inference
when the likelihood function is analytically or computationally intractable but it is possible to simulate data from the model. Many ABC algorithms are based on sampling the ABC posteriors, including acceptance-rejection sampling, importance sampling (IS), and MCMC [5]}.
We refer to [6]} and references therein for a comprehensive review of ABC.
